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- #1

- Jan 26, 2012

- 995

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**Problem**: Use contour integration to show that

\[\int_{-\infty}^{\infty}\frac{e^{-2\pi i x\xi}}{(1+x^2)^2}\,dx = \frac{\pi}{2}(1+2\pi|\xi|)e^{-2\pi|\xi|} \]

for all $\xi$ real.

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**Hint**:

*lower*half circle as the contour for this integral.

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